To simplify the expression:
4 2^-3 + 8 2^-2 + 5 * 2^-1

First, calculate the exponents:
2^-3 = 1/2^3 = 1/8
2^-2 = 1/2^2 = 1/4
2^-1 = 1/2

Now substitute the exponents back into the expression:
4 (1/8) + 8 (1/4) + 5 * (1/2)

Simplify each term:
4/8 + 8/4 + 5/2

Now simplify the fractions:
1/2 + 2 + 5/2

Combine the terms:
1/2 + 5/2 + 2 = 6/2 + 5/2 + 4/2 = 15/2

Thus, the simplified expression is 15/2 or 7.5.